Absolute Value Graphs WS

Front

What is the definition of an absolute value function?

Back

An absolute value function is a function that outputs the distance of a number from zero on the number line, regardless of direction. It is defined as f(x) = |x|.

Front

What does the graph of f(x) = |x| look like?

Back

The graph of f(x) = |x| is a V-shaped graph that opens upwards, with its vertex at the origin (0,0).

Front

How does the graph of f(x) = |x - h| + k transform the basic graph of f(x) = |x|?

Back

The graph shifts horizontally by h units and vertically by k units. If h is positive, it shifts right; if negative, left. If k is positive, it shifts up; if negative, down.

Front

What is the vertex of the function f(x) = |x + 4| + 3?

Back

The vertex is at the point (-4, 3).

Front

How does the coefficient of x in f(x) = a|x - h| + k affect the graph?

Back

The coefficient 'a' affects the vertical stretch or compression and the direction of the graph. If a > 1, the graph stretches; if 0 < a < 1, it compresses; if a < 0, it reflects over the x-axis.

Front

What transformation does the equation y = |x| - 7 represent?

Back

The graph of y = |x| - 7 is the graph of y = |x| shifted down 7 units.

Front

What is the equation of the absolute value function that has a vertex at (3, 4)?

Back

The equation is f(x) = |x - 3| + 4.

Front

How do you determine the transformations from the equation f(x) = |x - 2| + 5?

Back

The graph shifts right 2 units and up 5 units from the basic graph of f(x) = |x|.

Front

What is the effect of adding a constant outside the absolute value, such as in f(x) = |x| + 4?

Back

Adding a constant outside the absolute value shifts the graph vertically. In this case, it shifts the graph up 4 units.

Front

What is the equation of the absolute value function that opens downwards?

Back

An absolute value function cannot open downwards; it can only open upwards. However, if you want to reflect it, you can use f(x) = -|x|.